A205505 Fibonacci(n*(n+1)) / Fibonacci(n).

1, 8, 72, 2255, 166408, 33489287, 17373187209, 23735905327584, 84707858657965180, 792123204706451722511, 19386236394149894806708656, 1242293991563772001787883943693, 208405704482555536994509895576090977, 91533085042008706066658193727853843719640

Offset: 1

Author

Paul D. Hanna, Jan 28 2012

Keywords

• nonn
• easy

Crossrefs

Cf. A103624, A051294, A028412.

Programs

Mathematica

Table[Fibonacci[n(n+1)]/Fibonacci[n],{n,20}] (* Harvey P. Dale, Mar 30 2012 *)

PARI

{a(n)=fibonacci(n*(n+1))/fibonacci(n)}

PARI

{Lucas(n)=fibonacci(n-1)+fibonacci(n+1)}
{a(n)=polcoeff(1/(1-Lucas(n)*x+(-1)^n*x^2+x*O(x^n)), n)}

Formula

a(n) = [x^n] 1/(1 - Lucas(n)*x + (-1)^n*x^2), where Lucas(n) = A000204(n).

Forms a diagonal in table A028412.